The Pizza Problem
The Pizza Problem
Embedded Files
Mathematical Problem Solving
Mathematical Problem Solving
We were tasked to think of a new mathematical problem or a modified version of an existing one. Our group decided to make one employing the use of basic investigative skills and simple algebraic mathematics. In this problem we tackle a creative perspective on two relatable concepts in a scenario: eating pizza, and making sure you get fair divisions!
What Happened?
What Happened?
Yang, Enrique, and Margaux wanted to order a pizza for dinner. They called PizzaBox down the street to order their favorite pepperoni pizza. However, when the box of pizza arrived, they were faced with a dilemma. The 1 foot-square pizza was divided into quarters, but they were only three.
Margaux, being the “Math-Lord” of the group, suggested that to equally divide the pizza, she should take one fourth of the pizza, and another one fourth of the pizza should be divided into more fourths, where she would also take one fourth, and divide another fourth of the division into more fourths, taking one more fourth, and so on.
Yang and Enrique get confused about how that will be fair for all of them, but they are too shy to ask Margaux, how do they know that this division is fair and equal?
Use the figure to the right to help you in solving for the truth!
Solution
Solution
Below is the problem's solution and answer! Try to solve it on your own before checking your answers using the guided solution below!
Step 1
Step 1
First, to solve this problem, we must convert it into an equation. That way, it will be easier to solve!
Margaux’s share is shown as X in the equation where she gets a fourth, and a fourth is divided into four
more divisions, and she gets a fourth, and so on.
Step 2
Step 2
Next, we simplify the equation to it's exponential form to make it easier to understand without all the extra expressions.
Step 3
Step 3
After that, we multiply both sides by 4 to get 1 from a fraction in the left side of the equation.
Step 4
Step 4
This part shows the equation when it is multiplied by 4.
Step 5
Step 5
We then simplified the fractions and are left with this equation. What can you observe with the expressions after the number 1?
Step 6
Step 6
The expressions after 1, can be observed to be equal to x. To further simplify the equation, those expressions were subtituted with x.
Step 7
Step 7
Next, X is transposed to be subtracted from 4x.
Step 8
Step 8
Lastly, we divide both sides by 3 to get the final answer!
Conclusion
Conclusion
Since Margaux's share is equal to a third of the pizza, it is an equal share for all of them! Thanks for helping Yang and Enrique solve the problem. Now, they can both eat their shares of the pizza in peace.
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